A Note on the Kullback-Leibler Divergence for the von Mises-Fisher distribution
Tom Diethe
TL;DR
This paper derives the Kullback-Leibler divergence formula for the von Mises-Fisher distribution in arbitrary dimensions, providing a theoretical tool for statistical analysis involving directional data.
Contribution
It offers a new derivation of the KL-divergence specifically for the von Mises-Fisher distribution across multiple dimensions.
Findings
Provides a closed-form expression for KL-divergence of VMF distributions.
Facilitates statistical inference and model comparison for directional data.
Enhances theoretical understanding of VMF distribution properties.
Abstract
We present a derivation of the Kullback Leibler (KL)-Divergence (also known as Relative Entropy) for the von Mises Fisher (VMF) Distribution in -dimensions.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Stochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods